64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Bootstrap inference in functional linear regression models with scalar response under heteroscedasticity

Author

HY
Hyemin Yeon

Co-author

  • D
    Daniel John Nordman
  • X
    Xiongtao Dai

Conference

64th ISI World Statistics Congress - Ottawa, Canada

Format: CPS Abstract

Keywords: biascorrection, bootstrap, fda, heteroscedasticity, multipletesting, regression

Abstract

Despite its importance, inference about linear models based on regressors in function spaces have been less studied compared to the finite dimensional setting, particularly in the case of heteroscedasticity. At issue, mean (or projection) estimates have complicated sampling distributions, due to bias and scaling problems from infinite dimensional regressors, which is compounded by effects of non-constant variance. In fact, central limit theorems have not yet been established in this case. We develop a paired bootstrap method to approximate sampling distributions of estimated projections, as well as give a central limit theorem, when the errors have different conditional variances given the regressors. When the paired bootstrap is implemented in a standard fashion though, following the case of finite dimensional regressors, the bootstrap approximation can provably fail. The reason owes to bias from functional regressors in this bootstrap construction. A modified paired bootstrap is applicable, however, for constructing confidence intervals for projections and for conducting hypothesis tests for the slope function. Our theoretical results on bootstrap consistency are demonstrated through numerical studies. The paired bootstrap method is illustrated with real data examples.